1(a) Draw the FBD and the shear and bending moment diagrams for the beam shown in Figure I. Label all minimums, maximums and zero crossing points as well as the slopes as constant, linear or parabolic.
2. A simply supported beam is shown in Figure 2(a), and the cross-section is given in Figure 2(b).
(a) Draw the F130 for the structure and solve for the reactions. Cut the structure at point A (as seen in Figure 2(a)) and draw the FBI) and solve for the forces at point A.
(b) Use the parallel axis theorem to solve for the second moment of area, I, of the cross-section in
Figure 2(b).
(c) Solve for the normal stress and shear stress in the x and y directions and the principal stresses at point A (as illustrated in Figures 2(a) and 2(b)).
3. Use the moment area method to determine where along the beam, shown in Figure 3, the maximum deflection of the beam occurs using the moment diagram provided. Assume El = 1 x 1013 Nmmz. DO NOT solve for the maximum deflection.
4. The statically indeterminate beam in Figure 4 is supported by a pin at A, a spring with stiffness of 10000 N/mm at B and a roller at C. Use the force method to solve for the reactions at A, B and C. Assume El = 2 x 1013 Nmm2. The deflection equations for some common beams are also given below.
5. The column shown in Figure 5(a) is pinned at the bottom and is restrained against horizontal movement at the top. Based on the cross-section in Figure 5(b), a yield strength of 300 MPa, and a modulus of elasticity of 200 GPa, determine whether a load of P = 250kN with an eccentricity of 150 mm to the weak axis can be applied to the column safely.
6. For the frame shown in Figure 6, calculate the rotation at point A and B using virtual work. In your expert opinion, do these rotations seem reasonable? Assume El = 3 x 1013nmm2.
